1. Field of the Invention
The present invention relates to a device for controlling a running behavior of vehicles, and more particularly, to a device for conducting such a control of a four wheeled vehicle based upon a mathematical tire model simulating the performance of longitudinal and lateral forces vs. slip ratio of the tire of each wheel.
2. Description of the Prior Art
It is known in the art that the tires of the wheels of vehicles such as automobiles generally exhibit a performance such as exemplarily shown in the map of FIG. 5 with respect to the relationship between the longitudinal or lateral force and the slip ratio. Of course, the actual performance of each particular tire differs from the shown performance in the shape of the curves as well as in the magnitude of the scales according to its tread pattern and respective operational conditions such as a road surface condition, etc.
Further, it is also known in the art that such a performance between the longitudinal or lateral force and the slip ratio of the tires of wheels of vehicles can be mathematically simulated by the following equations: ##EQU1##
when .xi.i&gt;0, PA1 when .xi.i&lt;0, PA1 wherein, generalizing by i such suffixes as fr, fl, rr and rl indicating the pertinency to front right, front left, rear right and rear left wheels of a common four wheeled vehicle each bearing the tire, Ftxi and Ftyi are the longitudinal and lateral components of a force Fti acting at a tire (wheel) as illustrated in FIG. 6, and .theta.i is the angle between Fti and Ftxi, Si is a slip ratio of the tire defined as below by equation 5, and other parameters are as defined by the following: ##EQU2## PA1 wherein u is vehicle speed at the tire, R is radius of the tire, and .omega.is angular speed of the tire (-.infin.&lt;Si.ltoreq.1.0) ##EQU3## PA1 wherein .beta.i is slip angle of the wheel, Wi is vertical load on each wheel, Kb is the inclination at .beta.i=0 of a curve of the slip angle .beta.i vs. the lateral force Ftyi such as shown in FIG. 7 and Ks is the inclination at Si=0 of a curve of the slip angle Si vs. the longitudinal force Ftxi such as shown in FIG. 8. PA1 first means for cyclically calculating by a minute cycle period longitudinal force and lateral force of each of the at least either the front pair or the rear pair of the wheels in reference to slip ratio thereof according to a mathematical tire model of a relationship therebetween, so as to obtain a first longitudinal force and a first lateral force corresponding to a first slip ratio and a second longitudinal force and a second lateral force corresponding to zero slip ratio; PA1 second means for cyclically calculating by the minute cycle period longitudinal force, lateral force and yaw moment of the vehicle body based upon the longitudinal forces and the lateral forces of the at least either the front pair or the rear pair of the wheels, so as to obtain a first longitudinal force, a first lateral force and a first yaw moment of the vehicle body corresponding to the first longitudinal forces and the first lateral forces of the at least either the front pair or the rear pair of the wheels and a second longitudinal force, a second lateral force and a second yaw moment of the vehicle body corresponding to the second longitudinal forces and the second lateral forces of the at least either the front pair or the rear pair of the wheels; PA1 third means for cyclically modifying by the minute cycle period the second longitudinal force, the second lateral force and the second yaw moment of the vehicle body calculated by the second means with a longitudinal force, a lateral force and a yaw moment corresponding to an output of an outside running behavior controller, so as to obtain a nominal longitudinal force, a nominal lateral force and a nominal yaw moment, respectively; PA1 fourth means for cyclically calculating by the minute cycle period a difference between the nominal longitudinal force and the first longitudinal force, a difference between the nominal lateral force and the first lateral force and a difference between the nominal yaw moment and the first yaw moment; PA1 fifth means for cyclically calculating by the minute cycle period differentials of the longitudinal and lateral forces of each of the at least either the front pair or the rear pair of the wheels on the basis of the slip ratio thereof according to the mathematical tire model; PA1 sixth means for cyclically calculating by the minute cycle period differentials of the longitudinal force, lateral force and yaw moment of the vehicle body based upon differentials of the longitudinal and lateral forces of each of the at least either the front pair or the rear pair of the wheels on the basis of the slip ratio; PA1 seventh means for cyclically calculating by the minute cycle period a difference in the longitudinal force, a difference in the lateral force and a difference in the yaw moment of the vehicle body based upon the differentials thereof; PA1 eighth means for cyclically calculating by the minute cycle period a first difference between the difference in the longitudinal force calculated by the fourth means and the difference in the longitudinal force calculated by the seventh means, a second difference between the difference in the lateral force calculated by the fourth means and the differential-based difference in the lateral force calculated by the seventh means, and a third difference between the difference in the yaw moment calculated by the fourth means and the differential-based difference in the yaw moment calculated by the seventh means; PA1 ninth means for calculating by the minute cycle period differences in the slip ratio of each of the at least either the front pair or the rear pair of the wheels which minimize a weighted sum of squares of the first, second and third differences; and PA1 tenth means for selectively operating the brake means to change the slip ratio of each of the at least either the front pair or the rear pair of the wheels according to the difference thereof calculated by the ninth means. PA1 eleventh means for cyclically calculating by the minute cycle period a weighted sum of a square of each of the differences in the slip ratio calculated by the ninth means; PA1 wherein the ninth means are modified to calculate the differences in the slip ratio so that a sum of the weighted sum calculated by the ninth means and the weighted sum calculated by the eleventh means is minimized. PA1 Further, the above-mentioned device may further be modified such that it further comprises: PA1 twelfth means for cyclically calculating by the minute cycle period a weighted sum of a square of each of respective sums of the slip ratio and the change thereof calculated by the ninth means; PA1 wherein the ninth means are modified to calculate the differences in the slip ratio so that a sum of the weighted sum calculated by the ninth means and the weighted sum calculated by the twelfth means is minimized.
or
Ftxi=-.mu.Wi cos .theta.i (3) EQU Ftyi=-.mu.Wi sin .theta.i (4)
The above equations are mathematical analyses of the relationships among such parameters as the longitudinal and lateral forces, the slip ratio, the slip angle, the vertical load and the friction coefficient with respect to each single tire. On the other hand, the running behavior of a four wheeled vehicles is a matter of interrelations among such respective performances of the four wheels. FIG. 9 shows an example of the yaw moment applied to the vehicle body of a four wheeled vehicle by a braking of each of the four wheels when the vehicle is running out of a straight course.
It would be contemplated to apply the above mathematical analyses to the running behavior control of four wheeled vehicles by preparing certain maps of relationships between or among each two or three of those parameters. However, if a four wheeled vehicle is mathematically controlled of its running behavior based upon a mathematical tire model such as expressed by the above-mentioned equations 1-9, since at least 11 parameters will be incorporated in the mathematical control calculations even when only one of the front and rear pairs of the wheels are controlled about their braking, only a very rough discrete points simulation would be available even by using the most modern microcomputers employable for an automobile running behavior control from the view point of the convenience of construction and economy.